Question

You are trying to compare the Fahrenheit and Celsius scales and you have two examples: Temperature A is 50 degrees Celsius and 122 degrees Fahrenheit. Temperature B is 100 degrees Celsius and 212 degrees Fahrenheit. What graph models the relationship between the Fahrenheit and Celsius scales? What is an equation of the line in slope-intercept form?

Answer 1

http://openstudy.com/study#/updates/50607146e4b0583d5cd24a6f

Answer 2

I still don't get it can you help me

Answer 3

sure, you have a graph, and you have 2 points like so:

Answer 4

so x axis represents degrees celsius
y axis represents degrees farenheit
and our 2 points are (50, 122) and (100, 212)

following ok so far?

Answer 5

yep:)

Answer 6

cools, so the only equation we can solve with only 2 points is the equation of a STRAIGHT LINE...
(note: if we had 3 points we could solve a quadratic, 4points a cubic...etc)

so the equation of a straight line is ...@cutegirl ?
y = ???

Answer 7

y=5/9x+32 right?

Answer 8

yeah, but we have to solve it, not know it already... ;D

so eqn of a straight line is always: y = mx + c
where m = gradient
and c = y intercept ( y point when x = o)

Answer 9

so to solve m:
m = (y2 - y1) / (x2 - x1)
= ...?

Answer 10

100-50/212-122=50=90=5/9 right?

Answer 11

nope, our x values were 100 and 50... not our y values...
so flip it

Answer 12

ow so 9/5

Answer 13

perfect
now we have the value for m = 9/5
so we need to find c (y intercept)

... so our equation so far is:
y = mx + c
y = (9/5) x + c

so how do we find c? @cutegirl ?

Answer 14

can you help me im new with this lol

Answer 15

of course, happy to
so if our equation's y = (9/5) x + c
so to find c now, we need values for x and y (then the only unknown we are left with is c)
so we can use any point that is on our line
and we already know 2 points that are on our line
[remember "our 2 points are (50, 122) and (100, 212) "]

so pick either of those points and sub it into the equation

Answer 16

also, points are always written (x , y) if that helps

Answer 17

212,100
122,50

Answer 18

ok
so our equation is:
y = (9/5) x + c
and the point along this line that we'll use is:
(50, 122) as this is an (x, y) point/pair

so y = (9/5) x + c
122 = (9/5)* 50 + c

can you solve for c from here?

Answer 19

90?

Answer 20

32 i mean

Answer 21

122 = (9/5)* 50 + c
122 = 90 + c
122 - 90 = c = 32, yep, perfect

Answer 22

thanks you :))

Answer 23

so the slope intercept form of the relationship between farenheit (y) and celcius (x) is
y = (9/5)x + 32

Answer 24

all good hey, welcomes